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Submodular set function

Known as: Submodular, Submodular function 
In mathematics, a submodular set function (also known as a submodular function) is a set function whose value, informally, has the property that the… 
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Related topics

Related topics

33 relations
Active learning (machine learning)Alexander SchrijverArtificial intelligenceAutomatic summarization

Broader (1)

Combinatorial optimization

Papers overview

Semantic Scholar uses AI to extract papers important to this topic.
Review
2014
Review
2014
Submodular Function Maximization
Submodularity is a property of set functions with deep theoretical consequences and far– reaching applications. At first glance… 
Highly Cited
2008
Highly Cited
2008
Optimal approximation for the submodular welfare problem in the value oracle model
  • J. Vondrák
  • Symposium on the Theory of Computing
  • 2008
  • Corpus ID: 170510
In the Submodular Welfare Problem, m items are to be distributed among n players with utility functions wi: 2[m] → R+. The… 
Highly Cited
2007
Highly Cited
2007
Maximizing a Submodular Set Function Subject to a Matroid Constraint (Extended Abstract)
Let $f:2^{N} \rightarrow \cal R^{+}$ be a non-decreasing submodular set function, and let $(N,\cal I)$ be a matroid. We consider… 
Highly Cited
2001
Highly Cited
2001
A combinatorial strongly polynomial algorithm for minimizing submodular functions
This paper presents a combinatorial polynomial-time algorithm for minimizing submodular functions, answering an open question… 
Highly Cited
2000
Highly Cited
2000
A Combinatorial Algorithm Minimizing Submodular Functions in Strongly Polynomial Time
  • A. Schrijver
  • Journal of combinatorial theory. Series B (Print)
  • 2000
  • Corpus ID: 6285230
We give a strongly polynomial-time algorithm minimizing a submodular function f given by a value-giving oracle. The algorithm… 
Highly Cited
1982
Highly Cited
1982
An analysis of the greedy algorithm for the submodular set covering problem
AbstractWe consider the problem: min $$\{ \mathop \Sigma \limits_{j \in s} f_j :z(S) = z(N),S \subseteqq N\} $$ wherez is a… 
Highly Cited
1978
Highly Cited
1978
An analysis of approximations for maximizing submodular set functions—I
LetN be a finite set andz be a real-valued function defined on the set of subsets ofN that satisfies z(S)+z(T)≥z(S⋃T)+z(S⋂T) for… 
Highly Cited
1978
Highly Cited
1978
Minimizing a Submodular Function on a Lattice
This paper gives general conditions under which a collection of optimization problems, with the objective function and the… 
Highly Cited
1978
Highly Cited
1978
Best Algorithms for Approximating the Maximum of a Submodular Set Function
A real-valued function z whose domain is all of the subsets of N = {1,..., n is said to be submodular if zS + zT ≥ zS ∪ T + zS… 
Highly Cited
1978
Highly Cited
1978
Accelerated greedy algorithms for maximizing submodular set functions
Given a finite set E and a real valued function f on P(E) (the power set of E) the optimal subset problem (P) is to find S ⊂ E… 
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